The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 17
... manner , because ABD is a straight line , the angle DBE is equal to the angle EBA : wherefore † the angle DBE is equal to the A E * 10 Det . D † ! Ax . B C angle CBE , the less to the greater ; which is impossible : therefore two ...
... manner , because ABD is a straight line , the angle DBE is equal to the angle EBA : wherefore † the angle DBE is equal to the A E * 10 Det . D † ! Ax . B C angle CBE , the less to the greater ; which is impossible : therefore two ...
Page 20
... manner , it may be demonstrated that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR . If two straight lines ...
... manner , it may be demonstrated that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR . If two straight lines ...
Page 21
... manner if the side BC be bisected , and AC be produced to G , it may be demonstrated that the angle BCG , that is , the angle * ACD , is greater than the * 15 . 1 . angle ABC . Therefore , if one side , & c . Q. E. D. PROP . XVII ...
... manner if the side BC be bisected , and AC be produced to G , it may be demonstrated that the angle BCG , that is , the angle * ACD , is greater than the * 15 . 1 . angle ABC . Therefore , if one side , & c . Q. E. D. PROP . XVII ...
Page 22
... manner , it may be demonstrated , that BAC , ACB , as also CÁB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. * 3 . 1 . 5. 1 . PROP . XVIII . THEOR . * The greater side of every triangle is opposite ...
... manner , it may be demonstrated , that BAC , ACB , as also CÁB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. * 3 . 1 . 5. 1 . PROP . XVIII . THEOR . * The greater side of every triangle is opposite ...
Page 23
... BC . In the same manner it may be Because AD is equal † to AC , add BA to each , therefore † Const the whole BD is equal † to the two BA and AC . +2 Ax . demonstrated , that the sides AB , BC are greater BOCK I PROP . XX . 23.
... BC . In the same manner it may be Because AD is equal † to AC , add BA to each , therefore † Const the whole BD is equal † to the two BA and AC . +2 Ax . demonstrated , that the sides AB , BC are greater BOCK I PROP . XX . 23.
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole